Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Monday 29 June 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 160,810 x 11[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 fema… miss… e380000… nhs_glo… 1 gl34fe South West
## [90m 2[39m 111 2020-03-18 fema… miss… e380001… nhs_sou… 1 ne325nn North Eas…
## [90m 3[39m 111 2020-03-18 fema… 0-18 e380000… nhs_air… 8 bd57jr North Eas…
## [90m 4[39m 111 2020-03-18 fema… 0-18 e380000… nhs_ash… 7 tn254ab South East
## [90m 5[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 35 rm13ae London
## [90m 6[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 9 n111np London
## [90m 7[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bar… 11 s752py North Eas…
## [90m 8[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 19 ss143hg East of E…
## [90m 9[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bas… 6 dn227xf North Eas…
## [90m10[39m 111 2020-03-18 fema… 0-18 e380000… nhs_bat… 9 ba25rp South West
## [90m# … with 160,800 more rows, and 2 more variables: day [3m[90m<int>[90m[23m, weekday [3m[90m<fct>[90m[23m[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 12
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 43
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 62
## 33 2020-04-02 East of England 64
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 93
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 92
## 43 2020-04-12 East of England 101
## 44 2020-04-13 East of England 78
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 64
## 50 2020-04-19 East of England 67
## 51 2020-04-20 East of England 67
## 52 2020-04-21 East of England 75
## 53 2020-04-22 East of England 67
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 66
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 45
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 36
## 67 2020-05-06 East of England 31
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 33
## 70 2020-05-09 East of England 29
## 71 2020-05-10 East of England 22
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 26
## 76 2020-05-15 East of England 19
## 77 2020-05-16 East of England 26
## 78 2020-05-17 East of England 17
## 79 2020-05-18 East of England 25
## 80 2020-05-19 East of England 15
## 81 2020-05-20 East of England 26
## 82 2020-05-21 East of England 21
## 83 2020-05-22 East of England 13
## 84 2020-05-23 East of England 12
## 85 2020-05-24 East of England 17
## 86 2020-05-25 East of England 25
## 87 2020-05-26 East of England 14
## 88 2020-05-27 East of England 12
## 89 2020-05-28 East of England 17
## 90 2020-05-29 East of England 16
## 91 2020-05-30 East of England 9
## 92 2020-05-31 East of England 8
## 93 2020-06-01 East of England 17
## 94 2020-06-02 East of England 14
## 95 2020-06-03 East of England 10
## 96 2020-06-04 East of England 7
## 97 2020-06-05 East of England 12
## 98 2020-06-06 East of England 5
## 99 2020-06-07 East of England 9
## 100 2020-06-08 East of England 5
## 101 2020-06-09 East of England 6
## 102 2020-06-10 East of England 8
## 103 2020-06-11 East of England 0
## 104 2020-06-12 East of England 9
## 105 2020-06-13 East of England 5
## 106 2020-06-14 East of England 4
## 107 2020-06-15 East of England 7
## 108 2020-06-16 East of England 3
## 109 2020-06-17 East of England 7
## 110 2020-06-18 East of England 4
## 111 2020-06-19 East of England 7
## 112 2020-06-20 East of England 2
## 113 2020-06-21 East of England 3
## 114 2020-06-22 East of England 6
## 115 2020-06-23 East of England 4
## 116 2020-06-24 East of England 3
## 117 2020-06-25 East of England 0
## 118 2020-06-26 East of England 3
## 119 2020-06-27 East of England 0
## 120 2020-03-01 London 0
## 121 2020-03-02 London 0
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## 142 2020-03-23 London 63
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## 146 2020-03-27 London 130
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## 256 2020-03-18 Midlands 13
## 257 2020-03-19 Midlands 8
## 258 2020-03-20 Midlands 28
## 259 2020-03-21 Midlands 13
## 260 2020-03-22 Midlands 31
## 261 2020-03-23 Midlands 33
## 262 2020-03-24 Midlands 41
## 263 2020-03-25 Midlands 48
## 264 2020-03-26 Midlands 64
## 265 2020-03-27 Midlands 72
## 266 2020-03-28 Midlands 89
## 267 2020-03-29 Midlands 92
## 268 2020-03-30 Midlands 90
## 269 2020-03-31 Midlands 123
## 270 2020-04-01 Midlands 140
## 271 2020-04-02 Midlands 142
## 272 2020-04-03 Midlands 124
## 273 2020-04-04 Midlands 151
## 274 2020-04-05 Midlands 164
## 275 2020-04-06 Midlands 140
## 276 2020-04-07 Midlands 123
## 277 2020-04-08 Midlands 186
## 278 2020-04-09 Midlands 139
## 279 2020-04-10 Midlands 127
## 280 2020-04-11 Midlands 142
## 281 2020-04-12 Midlands 139
## 282 2020-04-13 Midlands 120
## 283 2020-04-14 Midlands 116
## 284 2020-04-15 Midlands 147
## 285 2020-04-16 Midlands 102
## 286 2020-04-17 Midlands 118
## 287 2020-04-18 Midlands 115
## 288 2020-04-19 Midlands 92
## 289 2020-04-20 Midlands 107
## 290 2020-04-21 Midlands 86
## 291 2020-04-22 Midlands 78
## 292 2020-04-23 Midlands 103
## 293 2020-04-24 Midlands 79
## 294 2020-04-25 Midlands 72
## 295 2020-04-26 Midlands 81
## 296 2020-04-27 Midlands 74
## 297 2020-04-28 Midlands 68
## 298 2020-04-29 Midlands 53
## 299 2020-04-30 Midlands 56
## 300 2020-05-01 Midlands 64
## 301 2020-05-02 Midlands 51
## 302 2020-05-03 Midlands 52
## 303 2020-05-04 Midlands 61
## 304 2020-05-05 Midlands 59
## 305 2020-05-06 Midlands 59
## 306 2020-05-07 Midlands 48
## 307 2020-05-08 Midlands 34
## 308 2020-05-09 Midlands 37
## 309 2020-05-10 Midlands 42
## 310 2020-05-11 Midlands 33
## 311 2020-05-12 Midlands 45
## 312 2020-05-13 Midlands 40
## 313 2020-05-14 Midlands 37
## 314 2020-05-15 Midlands 40
## 315 2020-05-16 Midlands 34
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## 317 2020-05-18 Midlands 34
## 318 2020-05-19 Midlands 34
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## 375 2020-03-18 North East and Yorkshire 2
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## 381 2020-03-24 North East and Yorkshire 8
## 382 2020-03-25 North East and Yorkshire 18
## 383 2020-03-26 North East and Yorkshire 21
## 384 2020-03-27 North East and Yorkshire 28
## 385 2020-03-28 North East and Yorkshire 35
## 386 2020-03-29 North East and Yorkshire 38
## 387 2020-03-30 North East and Yorkshire 64
## 388 2020-03-31 North East and Yorkshire 60
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## 413 2020-04-25 North East and Yorkshire 69
## 414 2020-04-26 North East and Yorkshire 65
## 415 2020-04-27 North East and Yorkshire 65
## 416 2020-04-28 North East and Yorkshire 57
## 417 2020-04-29 North East and Yorkshire 69
## 418 2020-04-30 North East and Yorkshire 57
## 419 2020-05-01 North East and Yorkshire 64
## 420 2020-05-02 North East and Yorkshire 48
## 421 2020-05-03 North East and Yorkshire 40
## 422 2020-05-04 North East and Yorkshire 49
## 423 2020-05-05 North East and Yorkshire 40
## 424 2020-05-06 North East and Yorkshire 51
## 425 2020-05-07 North East and Yorkshire 45
## 426 2020-05-08 North East and Yorkshire 42
## 427 2020-05-09 North East and Yorkshire 44
## 428 2020-05-10 North East and Yorkshire 40
## 429 2020-05-11 North East and Yorkshire 29
## 430 2020-05-12 North East and Yorkshire 27
## 431 2020-05-13 North East and Yorkshire 28
## 432 2020-05-14 North East and Yorkshire 31
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## 434 2020-05-16 North East and Yorkshire 35
## 435 2020-05-17 North East and Yorkshire 26
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## 437 2020-05-19 North East and Yorkshire 27
## 438 2020-05-20 North East and Yorkshire 22
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## 442 2020-05-24 North East and Yorkshire 26
## 443 2020-05-25 North East and Yorkshire 21
## 444 2020-05-26 North East and Yorkshire 21
## 445 2020-05-27 North East and Yorkshire 22
## 446 2020-05-28 North East and Yorkshire 21
## 447 2020-05-29 North East and Yorkshire 25
## 448 2020-05-30 North East and Yorkshire 20
## 449 2020-05-31 North East and Yorkshire 20
## 450 2020-06-01 North East and Yorkshire 17
## 451 2020-06-02 North East and Yorkshire 23
## 452 2020-06-03 North East and Yorkshire 23
## 453 2020-06-04 North East and Yorkshire 17
## 454 2020-06-05 North East and Yorkshire 18
## 455 2020-06-06 North East and Yorkshire 21
## 456 2020-06-07 North East and Yorkshire 14
## 457 2020-06-08 North East and Yorkshire 11
## 458 2020-06-09 North East and Yorkshire 12
## 459 2020-06-10 North East and Yorkshire 18
## 460 2020-06-11 North East and Yorkshire 7
## 461 2020-06-12 North East and Yorkshire 9
## 462 2020-06-13 North East and Yorkshire 10
## 463 2020-06-14 North East and Yorkshire 11
## 464 2020-06-15 North East and Yorkshire 9
## 465 2020-06-16 North East and Yorkshire 10
## 466 2020-06-17 North East and Yorkshire 9
## 467 2020-06-18 North East and Yorkshire 10
## 468 2020-06-19 North East and Yorkshire 6
## 469 2020-06-20 North East and Yorkshire 4
## 470 2020-06-21 North East and Yorkshire 4
## 471 2020-06-22 North East and Yorkshire 6
## 472 2020-06-23 North East and Yorkshire 7
## 473 2020-06-24 North East and Yorkshire 8
## 474 2020-06-25 North East and Yorkshire 3
## 475 2020-06-26 North East and Yorkshire 5
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## 528 2020-04-21 North West 76
## 529 2020-04-22 North West 86
## 530 2020-04-23 North West 85
## 531 2020-04-24 North West 66
## 532 2020-04-25 North West 65
## 533 2020-04-26 North West 55
## 534 2020-04-27 North West 54
## 535 2020-04-28 North West 57
## 536 2020-04-29 North West 62
## 537 2020-04-30 North West 59
## 538 2020-05-01 North West 45
## 539 2020-05-02 North West 56
## 540 2020-05-03 North West 55
## 541 2020-05-04 North West 48
## 542 2020-05-05 North West 48
## 543 2020-05-06 North West 44
## 544 2020-05-07 North West 49
## 545 2020-05-08 North West 42
## 546 2020-05-09 North West 30
## 547 2020-05-10 North West 41
## 548 2020-05-11 North West 35
## 549 2020-05-12 North West 38
## 550 2020-05-13 North West 25
## 551 2020-05-14 North West 26
## 552 2020-05-15 North West 33
## 553 2020-05-16 North West 32
## 554 2020-05-17 North West 24
## 555 2020-05-18 North West 31
## 556 2020-05-19 North West 35
## 557 2020-05-20 North West 27
## 558 2020-05-21 North West 27
## 559 2020-05-22 North West 26
## 560 2020-05-23 North West 31
## 561 2020-05-24 North West 26
## 562 2020-05-25 North West 31
## 563 2020-05-26 North West 27
## 564 2020-05-27 North West 27
## 565 2020-05-28 North West 28
## 566 2020-05-29 North West 20
## 567 2020-05-30 North West 19
## 568 2020-05-31 North West 13
## 569 2020-06-01 North West 12
## 570 2020-06-02 North West 27
## 571 2020-06-03 North West 22
## 572 2020-06-04 North West 22
## 573 2020-06-05 North West 16
## 574 2020-06-06 North West 26
## 575 2020-06-07 North West 20
## 576 2020-06-08 North West 20
## 577 2020-06-09 North West 16
## 578 2020-06-10 North West 16
## 579 2020-06-11 North West 16
## 580 2020-06-12 North West 11
## 581 2020-06-13 North West 9
## 582 2020-06-14 North West 15
## 583 2020-06-15 North West 15
## 584 2020-06-16 North West 13
## 585 2020-06-17 North West 10
## 586 2020-06-18 North West 13
## 587 2020-06-19 North West 7
## 588 2020-06-20 North West 11
## 589 2020-06-21 North West 6
## 590 2020-06-22 North West 10
## 591 2020-06-23 North West 13
## 592 2020-06-24 North West 13
## 593 2020-06-25 North West 11
## 594 2020-06-26 North West 2
## 595 2020-06-27 North West 1
## 596 2020-03-01 South East 0
## 597 2020-03-02 South East 0
## 598 2020-03-03 South East 1
## 599 2020-03-04 South East 0
## 600 2020-03-05 South East 1
## 601 2020-03-06 South East 0
## 602 2020-03-07 South East 0
## 603 2020-03-08 South East 1
## 604 2020-03-09 South East 1
## 605 2020-03-10 South East 1
## 606 2020-03-11 South East 1
## 607 2020-03-12 South East 0
## 608 2020-03-13 South East 1
## 609 2020-03-14 South East 1
## 610 2020-03-15 South East 5
## 611 2020-03-16 South East 8
## 612 2020-03-17 South East 7
## 613 2020-03-18 South East 10
## 614 2020-03-19 South East 9
## 615 2020-03-20 South East 13
## 616 2020-03-21 South East 7
## 617 2020-03-22 South East 25
## 618 2020-03-23 South East 20
## 619 2020-03-24 South East 22
## 620 2020-03-25 South East 29
## 621 2020-03-26 South East 35
## 622 2020-03-27 South East 34
## 623 2020-03-28 South East 36
## 624 2020-03-29 South East 55
## 625 2020-03-30 South East 58
## 626 2020-03-31 South East 65
## 627 2020-04-01 South East 66
## 628 2020-04-02 South East 55
## 629 2020-04-03 South East 72
## 630 2020-04-04 South East 80
## 631 2020-04-05 South East 82
## 632 2020-04-06 South East 88
## 633 2020-04-07 South East 100
## 634 2020-04-08 South East 83
## 635 2020-04-09 South East 104
## 636 2020-04-10 South East 88
## 637 2020-04-11 South East 88
## 638 2020-04-12 South East 88
## 639 2020-04-13 South East 84
## 640 2020-04-14 South East 65
## 641 2020-04-15 South East 72
## 642 2020-04-16 South East 56
## 643 2020-04-17 South East 86
## 644 2020-04-18 South East 57
## 645 2020-04-19 South East 70
## 646 2020-04-20 South East 87
## 647 2020-04-21 South East 51
## 648 2020-04-22 South East 54
## 649 2020-04-23 South East 57
## 650 2020-04-24 South East 64
## 651 2020-04-25 South East 51
## 652 2020-04-26 South East 51
## 653 2020-04-27 South East 40
## 654 2020-04-28 South East 40
## 655 2020-04-29 South East 47
## 656 2020-04-30 South East 29
## 657 2020-05-01 South East 37
## 658 2020-05-02 South East 36
## 659 2020-05-03 South East 17
## 660 2020-05-04 South East 35
## 661 2020-05-05 South East 29
## 662 2020-05-06 South East 25
## 663 2020-05-07 South East 27
## 664 2020-05-08 South East 26
## 665 2020-05-09 South East 28
## 666 2020-05-10 South East 19
## 667 2020-05-11 South East 25
## 668 2020-05-12 South East 27
## 669 2020-05-13 South East 18
## 670 2020-05-14 South East 32
## 671 2020-05-15 South East 24
## 672 2020-05-16 South East 22
## 673 2020-05-17 South East 18
## 674 2020-05-18 South East 22
## 675 2020-05-19 South East 12
## 676 2020-05-20 South East 22
## 677 2020-05-21 South East 15
## 678 2020-05-22 South East 17
## 679 2020-05-23 South East 21
## 680 2020-05-24 South East 17
## 681 2020-05-25 South East 13
## 682 2020-05-26 South East 19
## 683 2020-05-27 South East 18
## 684 2020-05-28 South East 12
## 685 2020-05-29 South East 21
## 686 2020-05-30 South East 8
## 687 2020-05-31 South East 12
## 688 2020-06-01 South East 11
## 689 2020-06-02 South East 13
## 690 2020-06-03 South East 17
## 691 2020-06-04 South East 11
## 692 2020-06-05 South East 11
## 693 2020-06-06 South East 10
## 694 2020-06-07 South East 12
## 695 2020-06-08 South East 8
## 696 2020-06-09 South East 10
## 697 2020-06-10 South East 11
## 698 2020-06-11 South East 5
## 699 2020-06-12 South East 6
## 700 2020-06-13 South East 6
## 701 2020-06-14 South East 7
## 702 2020-06-15 South East 7
## 703 2020-06-16 South East 11
## 704 2020-06-17 South East 8
## 705 2020-06-18 South East 4
## 706 2020-06-19 South East 6
## 707 2020-06-20 South East 5
## 708 2020-06-21 South East 3
## 709 2020-06-22 South East 2
## 710 2020-06-23 South East 8
## 711 2020-06-24 South East 6
## 712 2020-06-25 South East 4
## 713 2020-06-26 South East 3
## 714 2020-06-27 South East 2
## 715 2020-03-01 South West 0
## 716 2020-03-02 South West 0
## 717 2020-03-03 South West 0
## 718 2020-03-04 South West 0
## 719 2020-03-05 South West 0
## 720 2020-03-06 South West 0
## 721 2020-03-07 South West 0
## 722 2020-03-08 South West 0
## 723 2020-03-09 South West 0
## 724 2020-03-10 South West 0
## 725 2020-03-11 South West 1
## 726 2020-03-12 South West 0
## 727 2020-03-13 South West 0
## 728 2020-03-14 South West 1
## 729 2020-03-15 South West 0
## 730 2020-03-16 South West 0
## 731 2020-03-17 South West 2
## 732 2020-03-18 South West 2
## 733 2020-03-19 South West 4
## 734 2020-03-20 South West 3
## 735 2020-03-21 South West 6
## 736 2020-03-22 South West 7
## 737 2020-03-23 South West 8
## 738 2020-03-24 South West 7
## 739 2020-03-25 South West 9
## 740 2020-03-26 South West 11
## 741 2020-03-27 South West 13
## 742 2020-03-28 South West 21
## 743 2020-03-29 South West 18
## 744 2020-03-30 South West 23
## 745 2020-03-31 South West 23
## 746 2020-04-01 South West 22
## 747 2020-04-02 South West 23
## 748 2020-04-03 South West 30
## 749 2020-04-04 South West 42
## 750 2020-04-05 South West 32
## 751 2020-04-06 South West 34
## 752 2020-04-07 South West 39
## 753 2020-04-08 South West 47
## 754 2020-04-09 South West 24
## 755 2020-04-10 South West 46
## 756 2020-04-11 South West 43
## 757 2020-04-12 South West 23
## 758 2020-04-13 South West 27
## 759 2020-04-14 South West 24
## 760 2020-04-15 South West 32
## 761 2020-04-16 South West 29
## 762 2020-04-17 South West 33
## 763 2020-04-18 South West 25
## 764 2020-04-19 South West 31
## 765 2020-04-20 South West 26
## 766 2020-04-21 South West 26
## 767 2020-04-22 South West 23
## 768 2020-04-23 South West 17
## 769 2020-04-24 South West 19
## 770 2020-04-25 South West 15
## 771 2020-04-26 South West 27
## 772 2020-04-27 South West 13
## 773 2020-04-28 South West 17
## 774 2020-04-29 South West 15
## 775 2020-04-30 South West 26
## 776 2020-05-01 South West 6
## 777 2020-05-02 South West 7
## 778 2020-05-03 South West 10
## 779 2020-05-04 South West 17
## 780 2020-05-05 South West 14
## 781 2020-05-06 South West 19
## 782 2020-05-07 South West 16
## 783 2020-05-08 South West 6
## 784 2020-05-09 South West 11
## 785 2020-05-10 South West 5
## 786 2020-05-11 South West 8
## 787 2020-05-12 South West 7
## 788 2020-05-13 South West 7
## 789 2020-05-14 South West 6
## 790 2020-05-15 South West 4
## 791 2020-05-16 South West 4
## 792 2020-05-17 South West 6
## 793 2020-05-18 South West 4
## 794 2020-05-19 South West 6
## 795 2020-05-20 South West 1
## 796 2020-05-21 South West 9
## 797 2020-05-22 South West 6
## 798 2020-05-23 South West 6
## 799 2020-05-24 South West 3
## 800 2020-05-25 South West 8
## 801 2020-05-26 South West 11
## 802 2020-05-27 South West 5
## 803 2020-05-28 South West 10
## 804 2020-05-29 South West 7
## 805 2020-05-30 South West 3
## 806 2020-05-31 South West 2
## 807 2020-06-01 South West 7
## 808 2020-06-02 South West 2
## 809 2020-06-03 South West 7
## 810 2020-06-04 South West 2
## 811 2020-06-05 South West 2
## 812 2020-06-06 South West 1
## 813 2020-06-07 South West 3
## 814 2020-06-08 South West 3
## 815 2020-06-09 South West 0
## 816 2020-06-10 South West 1
## 817 2020-06-11 South West 2
## 818 2020-06-12 South West 2
## 819 2020-06-13 South West 2
## 820 2020-06-14 South West 0
## 821 2020-06-15 South West 1
## 822 2020-06-16 South West 2
## 823 2020-06-17 South West 0
## 824 2020-06-18 South West 0
## 825 2020-06-19 South West 0
## 826 2020-06-20 South West 2
## 827 2020-06-21 South West 0
## 828 2020-06-22 South West 1
## 829 2020-06-23 South West 1
## 830 2020-06-24 South West 1
## 831 2020-06-25 South West 0
## 832 2020-06-26 South West 1
## 833 2020-06-27 South West 01.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Sunday 28 Jun 2020.
1.6 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 10,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 8,
lab_pos_y = 30200,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
rotate_x +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -10.6150 -3.1282 -0.3629 3.6398 6.0423
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.835e+00 5.509e-02 87.77 <2e-16 ***
## note_lag 1.255e-05 5.625e-07 22.32 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 14.22788)
##
## Null deviance: 7548.82 on 57 degrees of freedom
## Residual deviance: 823.59 on 56 degrees of freedom
## (23 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 125.854275 1.000013
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 112.824973 140.022959
## note_lag 1.000011 1.000014
Rsq(lag_mod)
## [1] 0.8908981
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.4.0 lubridate_1.7.9
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.14
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.1.1
## [10] projections_0.5.0 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_1.0.0 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.0 tibble_3.0.1 ggplot2_3.3.2
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 selectr_0.4-2 ggsignif_0.6.0 ellipsis_0.3.1
## [5] rprojroot_1.3-2 snakecase_0.11.0 fs_1.4.1 rstudioapi_0.11
## [9] farver_2.0.3 fansi_0.4.1 splines_4.0.2 knitr_1.29
## [13] jsonlite_1.7.0 broom_0.5.6 dbplyr_1.4.4 compiler_4.0.2
## [17] httr_1.4.1 backports_1.1.8 assertthat_0.2.1 Matrix_1.2-18
## [21] cli_2.0.2 htmltools_0.5.0 prettyunits_1.1.1 tools_4.0.2
## [25] gtable_0.3.0 glue_1.4.1 Rcpp_1.0.4.6 carData_3.0-4
## [29] cellranger_1.1.0 vctrs_0.3.1 nlme_3.1-148 matchmaker_0.1.1
## [33] crosstalk_1.1.0.1 xfun_0.15 ps_1.3.3 openxlsx_4.1.5
## [37] lifecycle_0.2.0 rstatix_0.6.0 MASS_7.3-51.6 scales_1.1.1
## [41] hms_0.5.3 sodium_1.1 yaml_2.2.1 curl_4.3
## [45] gridExtra_2.3 stringi_1.4.6 kyotil_2019.11-22 boot_1.3-25
## [49] pkgbuild_1.0.8 zip_2.0.4 rlang_0.4.6 pkgconfig_2.0.3
## [53] evaluate_0.14 lattice_0.20-41 labeling_0.3 htmlwidgets_1.5.1
## [57] cowplot_1.0.0 processx_3.4.2 tidyselect_1.1.0 plyr_1.8.6
## [61] magrittr_1.5 R6_2.4.1 generics_0.0.2 DBI_1.1.0
## [65] pillar_1.4.4 haven_2.3.1 foreign_0.8-80 withr_2.2.0
## [69] mgcv_1.8-31 survival_3.1-12 abind_1.4-5 modelr_0.1.8
## [73] crayon_1.3.4 car_3.0-8 utf8_1.1.4 rmarkdown_2.3
## [77] viridis_0.5.1 grid_4.0.2 readxl_1.3.1 data.table_1.12.8
## [81] blob_1.2.1 callr_3.4.3 reprex_0.3.0 digest_0.6.25
## [85] webshot_0.5.2 munsell_0.5.0 viridisLite_0.3.0